Introduction to Mobile Robotics

Transcription

1 Introduction to Mobile Robotics Riccardo Falconi Dipartimento di Elettronica, Informatica e Sistemistica (DEIS) Universita di Bologna riccardo.falconi@unibo.it Riccardo Falconi (DEIS) Introduction to Mobile Robotics 1 / 37

2 From Industrial Robotics to Mobile Robotics Starting from the 70s, early industrial robots Used to replace men in case of hazardous/repetivity/easy tasks Typically used for tasks to be executed in loco Workspaces were modeled considering robots capabilities and constraints Riccardo Falconi (DEIS) Introduction to Mobile Robotics 2 / 37

3 From Industrial Robotics to Mobile Robotics Robotics for manipulation Imitates the human arms (and hands) functionalities Mobile Robotics Himitates the animals locomotion principles Definition A mobile robot is an automatic machine able to move into the surrounding environment. Riccardo Falconi (DEIS) Introduction to Mobile Robotics 3 / 37

4 Typical Applications Indoor applications Cleaning Service robotics (museums, shops, etc.) Surveillance Stockings in warehouses... Applicazioni Outdoor Military applications Demining Spatial and underwater exploration Civil protection and fire surveillance Automatic agricultural... Riccardo Falconi (DEIS) Introduction to Mobile Robotics 4 / 37

5 How it all started... Mobile robots starting from 40s Rockets V1 - V2 (inertial autopilots) Drive-by-wire Electric motors Remotely controlled tank 500 m far Riccardo Falconi (DEIS) Introduction to Mobile Robotics 5 / 37

6 Examples AGV automatic warehouse Moves pallets from the loading bay to the depot area and viceversa Inside a warehouse there could be more than 30 AGVs Automatic Guided Vehicle (AGV) Electric 80 Riccardo Falconi (DEIS) Introduction to Mobile Robotics 6 / 37

7 Examples Underwater robots Recover wreckage (Titanic) Pipes inspections Water pollution monitoring Space applications Realized starting from 1965 Highly autonomous Able to work without a supervisor Riccardo Falconi (DEIS) Introduction to Mobile Robotics 7 / 37

8 Examples Agricultural robots ( 2015) Mobile robots designed for agricultural purposes: structured environments (ad hoc orchads) large fields cultivated with cereals Riccardo Falconi (DEIS) Introduction to Mobile Robotics 8 / 37

9 Examples Hazardous robots Robot Pioneer Developed by Stanford University Chosen to explore Chernobyl nuclear plant First modular robot allowing to mount: a robotic arm + a gripper a stereo camera Riccardo Falconi (DEIS) Introduction to Mobile Robotics 9 / 37

10 Locomotion Principles Natural solutions are difficult to be replied from an engineering point of view Walking The rolling is the most efficient solution, but it is not present in nature Most of the robotic systems move using wheels or tracks The walking is the natural best approximation of the rolling Crawling Running Jumping Riccardo Falconi (DEIS) Introduction to Mobile Robotics 10 / 37

11 Locomotion Principles Human walking It approximates rolling of a regular polygon Side of the polygon equal to the step of the person The shortest the step is, the better the rolling is approximated Walking robots: can adapt to a variable environment move slow on flat surfaces overactuated Robot with wheels/tracks: move faster on flat surfaces cannot adapt to a wide range of enviromental conditions Riccardo Falconi (DEIS) Introduction to Mobile Robotics 11 / 37

12 Robot Modeling Riccardo Falconi (DEIS) Introduction to Mobile Robotics 12 / 37

13 Wheeled Mobile Robots - WMR The wheel is the most suitable solution adopted for many applications Three wheels are enough to ensure vehicle stability How many wheels? What kind of wheels? Fixed wheel Centered orientable wheel Castor wheel Swedish wheel Riccardo Falconi (DEIS) Introduction to Mobile Robotics 13 / 37

14 Space of the configurations The dimension of the space of the configurations is equal to the minimum number of parameters needed to localize the robot configuration It depens on the structure of the considered robot Example: Unicycle Y Example: Bicycle Y φ r y r θ r y r θ r x r X x r X q = [x r, y r, θ r ] T R 3 q = [x r, y r, θ r, φ r ] T R 4 Riccardo Falconi (DEIS) Introduction to Mobile Robotics 14 / 37

15 Anolonomous constraints Hipothesys Each wheel rolls without sliding Each wheel introduces a nonholonomic constraint in the system (it does not allow the robot to move perpendicularly to the rolling direction) Wheels reduce the instantaneous robot mobility without reducing the maneuvering capabilities (e.g. parallel parking) ψ y θ v n v t = ψr Without constraint: ( ẋ = v t cos θ + v n cos θ + π ) ( 2 ẏ = v t sin θ + v n sin θ + π ) 2 x As long as the sliding in the normal direction is not allowed v n = 0 { ẋ = vt cosθ tan θ = y [ ẋ sinθ ẏ cosθ = 0 ẏ = v t sinθ x Mobility constraint ] Riccardo Falconi (DEIS) Introduction to Mobile Robotics 15 / 37

16 Pfaffian constraint For each wheel the constraint can be written in a vectorial form as: a(q) q = 0 With N wheels, constraints can be expressed in matrix form as: A(q) q = 0 A constraint that can be written as A(q) q = 0 is called Pfaffian constraint Nonholonomic constraint It is not fully integrable It cannot be written in the space of the configurations It doesn t limit the mobility but only the instantaneous mobility of the robot Allowed velocities They can be generated by using a matrix G(q) such that: Im(G(q)) = Ker(A(q)), q C C = R N Riccardo Falconi (DEIS) Introduction to Mobile Robotics 16 / 37

17 Unicyle model Constraint: ẋ sinθ ẏ cosθ = [sinθ, cosθ, 0] q = 0 Pfaffian { form: A(q) q = 0 A(q) = [sinθ, cosθ, 0] con: q = [x, y, θ] T 02 Ker(A(q)) = 4 cos θ sin θ , 4 Unicycle kinematic model q = cosθ sinθ v ω = 0 1 v: wheel linear velocity ω: angular velocity A = Im(G(q)) cosθ 0 sinθ [ ] v ω Y y r y One orientable wheel x r x θ r X ω ψ v = ψr Riccardo Falconi (DEIS) Introduction to Mobile Robotics 17 / 37

18 Unicycle model The real unicycle has statics stability problems Structures kinematically equivalent are used Synchronized Drive model Parallel orientable and coupled wheels Inputs [v, ω] T [x,y, θ] T position and orientation. y Differential Drive model Two wheels indipendently driven A third wheel to ensure stability [x, y, θ] T position of the centerl of the robot + its orientation. y y r θ r y r θ r x r x x r x Riccardo Falconi (DEIS) Introduction to Mobile Robotics 18 / 37

19 Differential Drive unicycle model y Definite ω R = Right wheel velocity ω L = Left wheel velocity d = wheel axle r = wheel radius ω L θ r Inputs ω R, ω L [ ] [ v r = 2 ω r d r 2 r d ] [ ωr ω L ] y r d 2r ω R x r x State space model ẋ q = ẏ = cosθ 0 sin θ 0 θ 0 1 r [ 2 r d r 2 r d ] [ ] ωr = ω L r cos θ 2 r sin θ d r d r cos θ 2 r sin θ d r d [ ωr ω L ] Riccardo Falconi (DEIS) Introduction to Mobile Robotics 19 / 37

20 Mobile robot control Riccardo Falconi (DEIS) Introduction to Mobile Robotics 20 / 37

21 Control scheme Task Plan High-Level Control Low-Level Control + err. q Control d u τ Act. Sensors (Internal, Envirom.) Robot Model End Effector q F Environment Actuators (DC motors, step-by-step motot,...) End-Effector (gripper, hand, probe, etc.) Sensors Internal state (encoder, gyro,...) Enviromental (bumbers, rangefinders (infrared, ultrasuond), laser, vision (mono, stereo),...) Control Low level High level Riccardo Falconi (DEIS) Introduction to Mobile Robotics 21 / 37

22 Low level control Low-Level Control High level Control Control u Act. τ Robot Model Foundamentals High gain PI controllers are used to control robot motors such that it moves following the desired velocity profile If the gain is high enough, the low level control transforms the robot in a kinematic system Low level control is in charge of controlling the robot actuators following high level controller instructions Riccardo Falconi (DEIS) Introduction to Mobile Robotics 22 / 37

23 Low level vs. High level control Foundamentals The signal provided to the low level controller is computed by analyzing information gathered by sensors Control signals are velocities From a high level point-of-view the robot is considered as a kinematic system Task + err. High level Control q d High-Level Control High level it defines the robot behaviour it takes into account the kinematic model it is subject to wheels constraints it has to control a complex non linear system Low level it controls the motors usually it is a PI control (linear system) it is not affected by wheels constraints Riccardo Falconi (DEIS) Introduction to Mobile Robotics 23 / 37

24 Elementary motion action Point-to-point transfer Initial position Final position Trajectory Following Initial position Parameter s Trajectory Tracking Reference WMR Final position Initial position Reference WMR at time t Parameter t Final position Riccardo Falconi (DEIS) Introduction to Mobile Robotics 24 / 37

25 Motion control Two different problems Configuration Starting from an initial configuration q 0 = [x 0, y 0, θ 0 ] T, the robot has to reach a predefined desired configuration q d = [x d, y d, θ d ] T. More difficult but generic problem Trajectory Starting from an initial configuration q 0 = [x 0, y 0, θ 0 ] T that can be or not on the trajectory, the robot has to reply asymptotically a cartesian trajectory [x d (t), y d (t)] T : Trajectory Following if the problem is position-dependent (s) Trajectory Tracking if the problem is time-depentent (t) Simpler and more practical problem Riccardo Falconi (DEIS) Introduction to Mobile Robotics 25 / 37

26 Trajectory following - I-O SFL Basic idea To define a point b out of the wheels axis To control the point b The point b pulls the vehicle Y y b y r b θ r { xb = x r + b cosθ r y b = y r + b sinθ r, b 0 x r X x b X The point b has no constraints and it can move instantaneously in all the directions The point b can move sideways with respect to the forward direction It is possible to define two inputs to control v x,b and v y,b { ẋb = v x,b ẏ b = v y,b Riccardo Falconi (DEIS) Introduction to Mobile Robotics 26 / 37

27 Trajectory following - I-O SFL ẋ b = ẋ r b ω sin θ r = v cos θ r b ω sin θ r ẏ b = ẏ r + b ω cosθ r = v sin θ r + b ω cosθ r θ r = ω, b 0» ẋb ẏ b» cos θ b sin θr = sin θ b cos θ r» v ω It is possible to prove that if b 0, then det (T(b, θ r )) 0 the matrix T(b, θ r ) is always invertible» v = T(b, θ r) ω Y y b y r b X θ r [ v ω ] [ ] [ = T(b, θ r ) 1 ẋb = ẏ b cosθ sin θ r 1 b sinθ 1 b cosθ r x r x b ] [ ẋb ẏ b ] X Riccardo Falconi (DEIS) Introduction to Mobile Robotics 27 / 37

28 Trajectory following - I-O SFL From the previous relationships the following linear system can be calculated x b = v x,b y b = v The x and y moving directions of the y,b θ r = 1 b (v point b can be controlled indipendently y,b cosθ r v x,b sin θ r ) by using the inputs v x,b and v y,b Given a desired trajectory (x d ( ), y d ( )) to be followed, it is possible to define v x,b and v y,b in order to ensure the asymptotic trajectory tracking by using the following linear control laws: { ẋb = v x,b = ẋ d + K 1 (x d x b ) ẏ b = v y,b = ẏ d + K 2 (y d y b ) Error dynamics { ex = x By defining d x b e y = y d y b { ėx + K 1 e x = 0 ė y + K 2 e y = 0 { ex 0 e y 0 Riccardo Falconi (DEIS) Introduction to Mobile Robotics 28 / 37

29 Trajectory following - I-O SFL Once the inputs to control b have been defined, it is possible to calculate the control inputs to be provided to the unicycle in order to move b as desired [ v ω ] [ = cosθ sinθ r 1 b sinθ 1 b cosθ r ] [ ẋb ẏ b ] Riccardo Falconi (DEIS) Introduction to Mobile Robotics 29 / 37

30 Navigation Interaction with the environment Usually a robot has to move in an environment with static or moving obstacles. By exploiting its knowledge of the environment and by exploiting the data provided by the on-board sensors, the robot has to detect and avoid the obstacles in order to safety navigate the workspace, i.e. avoiding collisions. q goal qstart Navigation problem Given a starting and final configuration, the navigation problem deals with the possibility of finding a collision free path that can be followed by the robot in order to move from the starting to the final configuration. Riccardo Falconi (DEIS) Introduction to Mobile Robotics 30 / 37

31 Navigation: the Braitenberg Algorithm Valentino Braitenberg (Bolzano, 1924). Neuropsychiatric. A simple neural network elaborates the signals provided by the sensors on the right and left side of the robot and it applies the results directly to the motor Braitenberg, V. (1984) I veicoli pensanti. Saggio di psicologia sintetica. Garzanti, Milano Braitenberg, V. (1984) Vehicles: Experiments in synthetic psychology. Cambridge, MA: MIT Press. + + Riccardo Falconi (DEIS) Introduction to Mobile Robotics 31 / 37

32 Navigation: Potential Fields The path planning based on the potential field approach it it possible to plan the path even for fully actuated robots Potential fields allow to generate the the path incrementally by changing it every time an obstacle is detected Potential function Gradient of U U(q) = U : R m R [ U (q)... U ] T (q) q 1 q n q = [q 1, q 2] U(q) = 1 2 qt q U(q) = [q 1, q 2] U(q) is equivalent to an energy function defined over the space configuration U( ) represents the forces generated by the potential field U(q) points in the U growing direction Riccardo Falconi (DEIS) Introduction to Mobile Robotics 32 / 37

33 Navigation: Potential Fields Gradient descent Potential functions are like landscapes where the robot is immersed The robot has to move from a higher point to a lower point The robot has to follow a downhill path (negative gradient) U(q) q(t) = U(q) qstart qstart Local Minimum Global Minimum q q goal The robot moves in a potential field defined as the sum of all the potential field present in the environment Riccardo Falconi (DEIS) Introduction to Mobile Robotics 33 / 37

34 Navigation: Potential Fields To create the potential field to drive a robot from qstart to q goal while avoiding obstacles we have to consider two kind of potential fields Attractive Potential Field U att (q) It has the minimum is in q goal It has to attract the robot toward the goal position Repulsive Potential Field U rep = N obst i=1 U rep i (q) It is calculated as the sum of all the repulsive potential field generated by each obstacle It has to push the robot away from the obstacles Potential field based control law q(t) = U(q), dove: U(q) = U att (q) + U rep (q) Riccardo Falconi (DEIS) Introduction to Mobile Robotics 34 / 37

35 Navigation: Potential Fields Attractive Potential Field Monotonically increasing with (q, q goal ) Robot attracted in (q, q goal ) q goal isolated minimum: no critical points Example U att = 1 2 K a (q, q goal ) U att = 1 2 K a 2 (q, q goal ) = K a (q q goal ) When the robot is far from the goal, it moves slowly When the robot is close to the goal, it moves fast Riccardo Falconi (DEIS) Introduction to Mobile Robotics 35 / 37

36 Navigation: Potential Fields Repulsive Potential Field Given by the sum of the potential field associated to each obstacle The repulsive force increases as long as the robot moves closer to the obstacle The repulsive force is null after a certain predefined distance Example U repi (q) = U repi (q) = If d i(q) = 0, 8 < : 8 < : Kr i d 1 «2 d i(q) q i(q) q 0 d i(q) > q «2 d i(q) d i(q) q d i(q) 0 d i(q) > q K ri 1 q 1 then U rep(q) Local minima Riccardo Falconi (DEIS) Introduction to Mobile Robotics 36 / 37

37 Navigation: Potential Fields and Local Minima The algorithm based on the gradient descent could be stuck in a local minima, that is a particular configuration where attractive and repulsive field are equal q start Possible solutions Best first algorithm Best first randomized algorithm Navigation functions q goal This is not a complete planning method Except some particular cases, the local minima are always present Generically could be avoided by using convex obstacles Adding noise Escape window algorithm Riccardo Falconi (DEIS) Introduction to Mobile Robotics 37 / 37